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LCM of 40 and 50

LCM of 40 and 50 is the smallest number among all common multiples of 40 and 50. The first few multiples of 40 and 50 are (40, 80, 120, 160, 200, 240, 280, . . . ) and (50, 100, 150, 200, 250, 300, . . . ) respectively. There are 3 commonly used methods to find LCM of 40 and 50 - by prime factorization, by division method, and by listing multiples.

1.	LCM of 40 and 50
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 40 and 50?

Answer: LCM of 40 and 50 is 200.

Explanation:

The LCM of two non-zero integers, x(40) and y(50), is the smallest positive integer m(200) that is divisible by both x(40) and y(50) without any remainder.

Methods to Find LCM of 40 and 50

Let's look at the different methods for finding the LCM of 40 and 50.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 40 and 50 by Prime Factorization

Prime factorization of 40 and 50 is (2 × 2 × 2 × 5) = 2³ × 5¹ and (2 × 5 × 5) = 2¹ × 5² respectively. LCM of 40 and 50 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 5² = 200.
Hence, the LCM of 40 and 50 by prime factorization is 200.

LCM of 40 and 50 by Listing Multiples

To calculate the LCM of 40 and 50 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 40 (40, 80, 120, 160, 200, 240, 280, . . . ) and 50 (50, 100, 150, 200, 250, 300, . . . . )
Step 2: The common multiples from the multiples of 40 and 50 are 200, 400, . . .
Step 3: The smallest common multiple of 40 and 50 is 200.

∴ The least common multiple of 40 and 50 = 200.

LCM of 40 and 50 by Division Method

To calculate the LCM of 40 and 50 by the division method, we will divide the numbers(40, 50) by their prime factors (preferably common). The product of these divisors gives the LCM of 40 and 50.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 40 and 50. Write this prime number(2) on the left of the given numbers(40 and 50), separated as per the ladder arrangement.
Step 2: If any of the given numbers (40, 50) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 40 and 50 is the product of all prime numbers on the left, i.e. LCM(40, 50) by division method = 2 × 2 × 2 × 5 × 5 = 200.

☛ Also Check:

LCM of 40 and 50 Examples

Example 1: The product of two numbers is 2000. If their GCD is 10, what is their LCM?

Solution:

Given: GCD = 10
product of numbers = 2000
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2000/10
Therefore, the LCM is 200.
The probable combination for the given case is LCM(40, 50) = 200.
Example 2: Verify the relationship between GCF and LCM of 40 and 50.

Solution:

The relation between GCF and LCM of 40 and 50 is given as,
LCM(40, 50) × GCF(40, 50) = Product of 40, 50
Prime factorization of 40 and 50 is given as, 40 = (2 × 2 × 2 × 5) = 2³ × 5¹ and 50 = (2 × 5 × 5) = 2¹ × 5²
LCM(40, 50) = 200
GCF(40, 50) = 10
LHS = LCM(40, 50) × GCF(40, 50) = 200 × 10 = 2000
RHS = Product of 40, 50 = 40 × 50 = 2000
⇒ LHS = RHS = 2000
Hence, verified.
Example 3: The GCD and LCM of two numbers are 10 and 200 respectively. If one number is 40, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 40 × b
⇒ b = (GCD × LCM)/40
⇒ b = (10 × 200)/40
⇒ b = 50
Therefore, the other number is 50.

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FAQs on LCM of 40 and 50

What is the LCM of 40 and 50?

The LCM of 40 and 50 is 200. To find the least common multiple of 40 and 50, we need to find the multiples of 40 and 50 (multiples of 40 = 40, 80, 120, 160 . . . . 200; multiples of 50 = 50, 100, 150, 200) and choose the smallest multiple that is exactly divisible by 40 and 50, i.e., 200.

How to Find the LCM of 40 and 50 by Prime Factorization?

To find the LCM of 40 and 50 using prime factorization, we will find the prime factors, (40 = 2 × 2 × 2 × 5) and (50 = 2 × 5 × 5). LCM of 40 and 50 is the product of prime factors raised to their respective highest exponent among the numbers 40 and 50.
⇒ LCM of 40, 50 = 2³ × 5² = 200.

What is the Least Perfect Square Divisible by 40 and 50?

The least number divisible by 40 and 50 = LCM(40, 50)
LCM of 40 and 50 = 2 × 2 × 2 × 5 × 5 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 40 and 50 = LCM(40, 50) × 2 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

Which of the following is the LCM of 40 and 50? 10, 200, 40, 36

The value of LCM of 40, 50 is the smallest common multiple of 40 and 50. The number satisfying the given condition is 200.

If the LCM of 50 and 40 is 200, Find its GCF.

LCM(50, 40) × GCF(50, 40) = 50 × 40
Since the LCM of 50 and 40 = 200
⇒ 200 × GCF(50, 40) = 2000
Therefore, the greatest common factor (GCF) = 2000/200 = 10.

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